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An Improved Task Scheduling Algorithm
based on Max-min for Cloud Computing

Abstract

In this paper a unique modification to the Improved Max-min algorithm is proposed. In Improved Maxmin algorithm largest job is selected and assigned to the resource which gives minimum completion time. Here two algorithms are proposed on Improved Max-min where instead of selecting the largest task , a task just greater than average execution time is selected and assigned to the resource which gives minimum completion time. The experimental results shows the new algorithms schedules jobs with lower makespan .

Keywords

INTRODUCTION

Cloud computing has become a new age technology that has got huge potentials in enterprises and markets.
Cloud computing now is known as a provider of dynamic services using very large scalable , on demand, virtualized
resources over the internet. It also make it possible to access applications and associated data from anywhere.
Companies are able to rent resources from cloud for storage and other computational purposes so that their
infrastructure cost can be reduced significantly. They can also make use of software’s, platforms and infrastructures as
a services , based on pay-as-you-go model.

Some of the drawbacks of the cloud computing is data centre network structure expansibility, energy
conservation, replica policies, security and scheduling mechanism [1] [2] [3]. The primary objective of this paper is
optimizing the scheduling polices. In cloud computing optimum scheduling is related to optimizing the resources being
allocated. Because of the uniqueness of the model, resource allocation is performed with the objective of minimizing
the costs associated with it. To make a set of cloud services an effective efficient provider infrastructure one of its
requirements is an effective Task scheduling algorithm. Task scheduling algorithm is responsible for mapping jobs
submitted to cloud environment onto available resources in such a way that the total response time ,the makespan is
minimized [4]

One of the feature of the Max-min algorithm is it selects the largest job and is executed on the fastest available
resource. The main drawback of the algorithm is it delays the execution of the smaller jobs and because of the dynamic
nature of the cloud , execution of the smaller jobs may be postponed indefinitely. Solution to this is improved Max-min
, it works well for the given set of jobs but dynamic cloud environment where the jobs are submitted at any time the
algorithm results in degradation in the performance.

In this paper we are proposed two algorithms to increase the efficiency of improved Max-min. The remaining
part of the paper are organized as follows : section II presents some related works on Max-min algorithm. Section III
presents our proposed modified two algorithms on Improved Max-min algorithm , Section IV describes the
Experimental results where we compare the result of the proposed algorithm with other Max-min algorithms. Finally
Section V concludes the paper and presents future work.

II. RELATED WORKS

2.1 Max-min Algorithm:

The Max-min Algorithm is based on “select a task with maximum execution time and assign to the resource with
minimum execution time”

2.2 Improved Max-min Algorithm[5]

The Max-min Algorithm is based on “select a task with maximum execution time and assign to the resource which
gives minimum completion time”

2.3 Enhanced Max-min Algorithm [6]

Some times in a mata-task largest task is too large compare to the other tasks . It may result in increase in the overall
makespan . Here a solution is proposed, first by selecting the job just greater than the average execution time and
assigning to the slowest resource and then executing the improved Max-min algorithm.

Max-min Algorithm gives priority to the larger tasks , first it assigns the time consuming jobs to the resources.
The main disadvantage of this algorithm is early execution of the large task might increase the total response time of
the system. A solution to this is the improved Max-min algorithm which is based on the completion time. Further the
result is improved in Enhanced Max-min algorithm first executing largest job in the slowest resource and then using
the improved Max-min. In the dynamic environment of the cloud, jobs are submitted batch wise. Always first selected
largest job is the largest job within the batch , when there are multiple batches of job this algorithm does not give the
efficient result.

III. PROPOSED ALGORITHM

The proposed algorithm is the improvement over to the Improved Max-Min algorithm [5], here the initial step of
Enhanced Max-Min Task scheduling algorithm [6] is considered. In Enhanced Max-Min ,first largest task ,just greater
than the average execution time is selected and is assigned to the slower resource then the Improved Max-min
algorithm is followed. Our proposed algorithm is the modification of the Improved Max-min algorithm where the
Largest task just greater than the average execution time is selected every time . Here we are proposing two algorithms
In algorithm 1 average execution time is calculated using the arithmetic mean and in algorithm 2 geometric mean is
used. Here arithmetic mean and geometric means are used because if the values are independent then arithmetic mean
is the best average. If the values are dependent on other values then the geometric mean is the best average. In cloud
environment jobs may be independent or dependent of each other and completion time of the job depend on the
completion time of the other jobs.

2.6. Update Cij for all j.

IV. EXPERIMENTAL RESULTS

We have used the Inspiral_100 , Montage_100 and Sipht_100 workflows to test our algorithm. Makespan
and average utilization of the resource are used to evaluate the performance of the algorithm. The Makespan of a
workflow is the time elapsed from its submission to the cloud until the completion of its last task. For the multiworkflow
scheduling experiments, in which a number of concurrent instances of a workflow are submitted to the cloud,
we consider the metric Total Makespan, which is the time elapsed from the submission of the instances until all the
instances are completed.

Here we considered two resources R1 and R2 with the processing speed 100 and 400 MIPS respectively. The
tool used to simulate the experiments is WorkflowSim. WorkflowSim is a workflow simulator to support large-scale
scheduling, clustering and provisioning studies. It extends the existing CloudSim simulator [7] by providing a higher
layer of workflow management. It also ignore system overheads and failures in simulating scientific workflows could
cause significant inaccuracies in the predicted workflow runtime.

The Table 1 shows the comparison of makespan of various versions of Max-min algorithms. The Results
shows that our proposed algorithms gives better results

V. CONCLUSIONS AND FUTURE WORK

When we use Max-min algorithm always largest task will be assigned to the best available resource (fastest)
and does not consider the completion time .In Improved Max-min completion time is considered and it assigns the
largest task to the resource which gives minimum completion time. In cloud computing users any time can submit the
job for execution and environment is dynamic. Cloud resource broker considering the dependency between the jobs ,
jobs are submitted batch wise dynamically[7] . Experimental results shows that instated of selecting the largest job
every time selecting the average sized jobs results in better makespan and average utilization of resources.

The Study can be further extended by considering the nature of the jobs in the joblist – homogeneous or
heterogeneous in size, the complexity still it can be improved. And also fault tolerance can be considered , because
after a job is submitted to the resource , if the resource becomes unavailable it may affect the makespan and average
utilization of the resource.

ACKNOWLEDGEMENT

The authors would like to thank the dedicated research group in the area of Cloud & Grid Computing , wireless
networks at the Dept of Computer Science, Mangalore University, Mangalore, India, for many stimulating discussions
for further improvement and future aspects of the Paper. Lastly but not least the author would like to thank everyone,
including the anonymous reviewers.